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Solved
List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...
1 day ago
Solved
List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...
1 day ago
Solved
Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...
1 day ago
Solved
Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...
1 day ago
Solved
Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...
1 day ago
Solved
List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...
1 day ago
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List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...
1 day ago
Solved
Estimating Battery Lifetime Based on Load Profile and Depth of Discharge (DoD)
In a Battery Management System (BMS), the lifetime of a battery depends on various factors, including the Depth of Discharge (Do...
1 day ago
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Estimating the Range of an Electric Vehicle (EV)
In Electric Vehicles (EVs), the driving range is the estimated distance a vehicle can travel on a fully charged battery. The ran...
1 day ago
Solved
Estimating Battery Backup Time for an Inverter
In a Battery Management System (BMS), estimating the backup time of a battery-powered inverter helps determine how long it can s...
1 day ago
Solved
Battery Charge Rate Calculation
In a Battery Management System (BMS), the charge rate () of a battery can be calculated using the formula: where: is th...
1 day ago
Solved
Battery State of Health (SoH) Calculation
In a Battery Management System (BMS), the State of Health (SoH) of a battery is an indicator of its overall condition. It is cal...
1 day ago
Solved
Battery Charge Efficiency Calculation
In a Battery Management System (BMS), the efficiency of battery charging can be estimated using the formula: where: is the...
1 day ago
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Battery Voltage Drop Estimation
In a Battery Management System (BMS), the voltage drop (V_drop) due to the load can be calculated using the formula:V_drop=I×R ...
1 day ago
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Battery Discharge Time Estimation
In a Battery Management System (BMS), the estimated discharge time (T) of a battery can be calculated as: where: is the ...
1 day ago
Solved
State of Charge (SoC) Estimation for a Battery
The State of Charge (SoC) of a battery represents its remaining charge as a percentage. It can be calculated using the formula: ...
1 day ago
Solved
Battery Life Estimation for a Device
A battery-powered device consumes a constant current while operating. The estimated battery life (T) can be calculated using the...
1 day ago
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X-intercepts of a quadratic.
Find the y value of the quadratic of the function at a point x.
1 day ago
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Estimating Monthly Electricity Cost for a Household Appliance
You recently bought an electric kettle for your kitchen, and you want to estimate how much it costs to run every month. The kett...
1 day ago
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Voltage Divider Calculation
A voltage divider is a simple circuit used to obtain a reduced voltage from a higher voltage source using two resistors in serie...
1 day ago
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LED Current Calculation
In an electrical circuit, the current (III) flowing through an LED is determined using Ohm’s Law: Where: I is the current ...
1 day ago
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Inductor Energy Storage Calculation
The energy (EEE) stored in an inductor is given by the formula: Where: E is the energy in joules (J) L is the inductance in...
1 day ago
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Calculate Charge Using Capacitance and Voltage
The charge (Q) stored in a capacitor is given by the formula:Q=C×V where: C is the capacitance (in farads) V is the voltage (...
1 day ago
Solved
Energy Stored in a Capacitor
The energy (E) stored in a capacitor is given by the formula: where: C is the capacitance (in farads) V is the voltage (in ...
1 day ago
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Calculate Current in a Series Circuit Using KVL
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop is zero. Given a voltage source (V) and three...
1 day ago
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Calculating the Total Resistance in a Series Circuit
Description: In a series circuit, the total resistance is the sum of the individual resistances. This problem asks you to write ...
1 day ago
Solved
Simple Electrical Power Calculation
Calculate the electrical power using the formula: P=V×I where: V is the voltage (in volts) I is the current (in amperes)
1 day ago
Solved
Ohm’s Law - Calculate Resistance
Ohm’s Law states that resistance R can be calculated as:R=V/I where: V is the voltage (in volts) I is the current (in ampere...
1 day ago
